I Want to be a Mathematician: An Automathography

428 Pages·1985·24.08 MB·English

by  Paul R. Halmos (auth.)

I WANT TO BE A MATHEMATICIAN
Paul R. Halmos
IWANTTOBEA
MATHEMATICIAN
An Automathography
With 43 Photographs
Springer Science+Business Media, LLC
Paul R. Halmos
Department of Mathematics
University of Santa Clara
Santa Clara, CA 95053
U.S.A.
AMS Subject Classifications: 01A65, 01A70, 0lA80
Library of Congress Cataloging in Publication Data
Halmos, Paul R. (Paul Richard)
I want to be a mathematician.
Includes index.
1. Halmos, Paul R. (paul Richard),
2. Mathematicians- United States- Biography.
1. Title.
QA29.H19A35 1985 510'.92'4 [B] 84-26688
© 1985 by Springer Science+Business Media New York
Originally published by Springer-Verlag New York Inc. in 1985
Softcover reprint ofthe hardcover Ist edition 1985
AII rights reserved. No part of this book may be translated or reproduced in any form
without written permission from Springer Science+Business Media, LLC .
Typeset by Composition House Ltd., Salisbury, England.
9 8 7 6 5 4 321
ISBN 978-0-387-96470-6 ISBN 978-1-4612-1084-9 (eBook)
DOI 10.1007/978-1-4612-1084-9
Dedication
To Ambrose, Doob, and von Neumann, who,
without knowing it, made me what I am today.
Overture
This is an automathography, a mathematical biography written by
its subject. It is definitely not a mathematics book, and, even more def
initely, it is not the story of my origins and my life. Sure, I had parents
(two), and wives (two, one at a time, the present one for forty years), and
cats (eight, two at a time, the present two for three years). I had and
have many faults, and, I'm pretty sure, a few virtues. I like Haydn, long
walks, Nero Wolfe, and dark beer, and for a few years I tried TM. All
that is true, but it's none of your business-that's not what this book is
about.
The book is about the career of a professional mathematician from
the 1930's to the 1980's. It is presented, more or less, in chronological
order, from high school to retirement, but its sections are organized by
substance rather than time. It tells about the University of Illinois, the
Institute for Advanced Study, and the universities commonly identified
as Chicago, Michigan, and Indiana. It expresses prejudices, it tells an
ecdotes, it gossips about people, and it preaches sermons. It tells about
taking prelims, looking for a job, writing a book, travelling, teaching,
and editing.
Fifty years ago I was cocky, iconoclastic, eager, ambitious, in a
hurry, ignorant, insecure. I have slowed down, mellowed (?), and learned
a few things. To some extent the book is from the me of today to the me
of yore, revealing some of the secrets that I desperately wanted to know
then.
P.R.H.
Thanks
Six people read every word of a typescript version of this book. Their
comments (cut this out-who was he?-not so had-tone it down-are
you sure?) cheered me up, or made me mad, hut, in either case, spurred
me on. They are John Ewing, Elena Fraboschi (who typed it all,
much of it several times), Leonard Gillman, Virginia Halmos, Walter
Kaufmann-Biihler, and Peter Rosenthal. Everything they said helped,
and I am truly grateful for their help. Thanks a lot.
Table of Contents
Part I. Student
CHAPTER I
Reading and writing and 'rithmetic
Words 3
Books 5
Writing 7
Languages 9
Numbers 10
Study or worry 12
Learning English 14
High school 16
CHAPTER 2
A college education
Move to Chambana , 20
How not to be a freshman 22
Trig and anaJyt 24
Calculus, and is there a doctor on the faculty? 26
Elementary mathematics and culture 28
Mathematical daydreams and BARBARA, 30
All Gaul 3]
A Bachelor of Science 33
XI
XII TABLE OF CONTENTS
CHAPTER 3
Graduate school
Statistics 36
The end of the affair 37
Matrices 40
The Dean 41
First class 43
Hazlett and Netzorg 45
Good morning, analysis 47
Why geometry? 48
CHAPTER 4
Learning to study
Doob arrives 50
All work and politics . 52
Born again. 55
Other forces, other tongues 57
Prelims 60
For example 61
Statistics, no 64
Readings and ratings 66
Reprints: Doob's and others' 67
Study 69
CHAPTER 5
Learning to think
Optional skipping 74
Roller coaster 76
Jobs, no 78
On my own 80
The end of an era . 82
CHAPTER 6
The Institute
The common room 84
The center of the world 88
Insignificant people 89
Work 91
Work and between work. 93
A weak paper and a pretty good book. 95
Collaboration 97
Measures and Harvard 98
Classical mechanics 100
Birthdays 101
TABLE OF CONTENTS XIlI
CHAPTER 7
Winning the war
Back home in Illinois . 105
Meetings 106
Teaching at Syracuse . 108
Research at Syracuse . III
Radiation Laboratory. 114
Referee and review 118
From Syracuse to Chicago 121
Part II. Scholar
CHAPTER 8
A great university
Eckhart Hall 127
Days of glory 129
What makes a great university? . 131
Teaching 133
Students and visitors . 137
CHAPTER 9
The early years
Guggenheim 140
111easure Theory 143
Master's exams 144
Judgments . 146
Jimmie Savage. 149
Students and courses 152
The beginning of Hilbert space 156
Ph.D. students. 159
The Cambridge Congress. 162
Follow the sun. 164
CHAPTER 10
Montevideo
Where to go? . 167
Saturation in Spanish . 170
Room and board . 172
Weather and climate . 177
How to get a chair 178
Humanities and sciences 179
Faculty of engineering 182